In perturbative QCD approach, we study the direct $CP$ violation in the decay of $\bar{ B}_s^0\to\rho(\omega )\phi\to { \pi^+}{ \pi^-}\phi$ via isospin symmetry breaking. An interesting mechanism involving the charge symmetry violating between $\rho$ and $\omega$ is applied to enlarge the $CP$ violating asymmetry. We find that the $CP$ violation can be enhanced by the $\rho-\omega$ mixing mechanism when the invariant masses of the $\pi^+\pi^-$ pairs are in the vicinity of the $\omega$ resonance. For the decay process of $\bar{ B}^0_{ s}\to\rho(\omega )\phi\to{ \pi^+}{ \pi^-}\phi$, the maximum $CP$ violation can reach $5.98\%$. The possibility of detecting the $CP$ violation is also presented.
Categories: hep-ph